In 2004, Facebook launched to little fanfare. Today, approximately 25% of the world’s population uses it every month, and Facebook describes its mission as to create a "global community for bringing people today,"

In this lesson, students write a quadratic function to model the number of possible connections between users on a social network. They use information about how Facebook has grown over time to determine how the number of connections has changed, and consider how well Facebook is living up to its mission: Does it help to connect us, or does it create echo chambers that leave us more separated?

### Students will

• Calculate the number of connections that can be formed in a small group of people
• Derive a general formula for the number of connections in a network with p people in it, and use this as a proxy for a network’s value
• Estimate Facebook’s value over time based on the growth of its user base
• Discuss whether a large social network is better for users or advertisers
• Explore an alternative to Facebook’s social network model, and discuss which approach is more valuable

### Before you begin

Students should be able to write and evaluate quadratic functions. The beginning of the lesson can be used to introduce some basic concepts from graph theory (such as edges and vertices), though the lesson can also be used without making any explicit mention of these ideas.